A parallel plate capacitor with air between the plates is charged to a potential difference of $500 V$ and then insulated. A plastic plate is inserted between the plates filling the whole gap. The potential difference between the plates now becomes $75 V$ . The dielectric constant of plastic is :

10 / 3

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5

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20 / 3

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10

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Solution

The correct option is C $20 / 3$
If $C$ be the air filled capacitance , dielectric filled capacitance becomes $C^{'} = K C$ where K is the dielectric constant.
Initial charge , $q_{i} = C V_{i} = 500 C$ and final charge $q_{f} = C^{'} V_{f} = 75 K C$
As the system is isolated so charge will be constant.
Thus, $q_{i} = q_{f}$
$\Rightarrow 500 C = 75 K C \Rightarrow K = \frac{500}{75} = 20 / 3$

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